Hammers boss Sam Allardyce had spoken optimistically about the prospect of tying up a deal for the 30-year-old Holland international, who has made only two appearances for the Toffees - both in the Capital One Cup - so far this season.
But in a statement released by his agents Sport Promotion on Thursday Heitinga said he had not been convinced that transfer would be right for him and had therefore called it off.
He added that he was confident, with the interest being shown in him, that he would be able to join another club before the end of the January transfer window.
"At my age it is important to make the right choices," Heitinga, whose current Everton contract runs out at the end of the season, said.
"Then it is not just about money, because that was not a problem at West Ham United.
"You must be convinced that you are making a right step and that (thought) was with me, so I cancelled (the move to) West Ham and we now await the interest of other clubs.
"There is some, so I'm confident that I can find another club before January 31.''
The statement by Sport Promotion made reference to the fact that West Ham are currently 19th in the Barclays Premier League table.
It also said of Heitinga: "His future may lie in England, but he is also open to a departure to another top league in Europe."
And the player spoke about his desire to play for his country at this summer's World Cup.
"I want to play in every game again, because I still have a huge appetite for the ball," Heitinga said.
"I am fit and, as a footballer, in the prime of my life.
"Moreover, I would like later to go to the World Cup in Brazil.
"I know that coach Louis van Gaal more or less has the condition that the players he selects are playing every week.
"This is not happening at Everton, so I'm looking at other options for a successful continuation of my career."
Heitinga, capped 87 times by Holland, joined Everton in 2009 from Atletico Madrid and had previously played for Ajax.
He made 30 appearances for the Toffees last season, when they were still managed by David Moyes, who was succeeded by Roberto Martinez over the summer.